Journal of Lie Theory 23 (2013), No. 2, 313--355
Copyright Heldermann Verlag 2013
Six-Dimensional Lie Algebras with a Five-Dimensional Nilradical
Anastasia Shabanskaya
Dept. of Mathematics and Computer Science, Eastern Connecticut State University, 83 Windham Street, Willimantic, CT 06226, U.S.A.
shabanskayaa@easternct.edu
Gerard Thompson
Dept. of Mathematics, The University of Toledo, 2801 W Bancroft St., Toledo, OH 43606, U.S.A.
gerard.thompson@math.utoledo.edu
This paper attempts to correct and simplify an old paper by G. M. Mubarakzyanov which classifies the six-dimensional indecomposable solvable Lie algebras for which the nilradical is five-dimensional. Mubarakzyanov discerned nine classes of such algebras depending on the isomorphism class of the nilradical. Each of these nine classes is re-examined. Many errors are corrected and a few algebras are shown to be redundant. In many cases some parameters can be removed completely. In addition the range of values of the parameters that occur in many classes are reduced, an issue which Mubarakzyanov did not treat very systematically.
Keywords: Solvable six-dimensional Lie algebra, nilradical.
MSC: 17B99
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